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• Associate Professor Earl Bardsley and Dr Adrian Pittari are in the University of Waikato's school of science.

The November 14 Kaikoura earthquake and its widespread damage is a reminder that nature imposes a running cost on all our infrastructure.

There are a variety of different natural hazards, with bigger hazards and bigger effects being further apart in time. For example, in New Zealand significant floods might occur every 10 years or so, and significant earthquakes roughly every 100 years. For even larger events over longer time intervals there are significant volcanic eruptions, such as the Taupo eruptions, every few thousand years.

All extreme natural events have a real or potential impact on our infrastructure, and long-term planning for these events must take account of both the impacts and frequencies of the events. It's possible that your car could be destroyed by a meteorite, but the waiting time for the next meteorite is so long it would be a waste of money to rush to build a meteorite-proof garage.

Nature's running cost can be thought of as the long-term average of repair costs caused by all natural events, both large and small. This would include, for example, the cost of rectifying the recently discovered leak in the Wellington water supply, thought to be a consequence of the Kaikoura earthquake.

Ultra-large events, such as asteroid impacts, have tiny probabilities and are no more likely to happen at one place in New Zealand than another, so the only infrastructure strategy needed is to forget all about them. However, things get more interesting when there is a geographical variation of probabilities of the events that occur more frequently.

We then have to think about the best strategy to minimise the long-term running cost.

For example, a bridge might be flooded relatively frequently and require repairs from time to time. Is it more cost-effective in the long term to spend more to build a new bridge higher above the river, or just leave the bridge as is and go on making repairs at the same rate as before?

Similarly, the decision to reopen State Highway 1 along the Kaikoura coast implies keeping it open not just with respect to repairing the damage of the November earthquake, but also to repair damage from future earthquakes. This is because it would not be logical to spend millions of dollars to re-establish the highway now, only to abandon it after the impact of the next major earthquake - and there is a next earthquake coming sometime. There are always alternatives. It might happen, for example, that a Kaikoura coast cycleway would bring more visitor stays along the coast, with a new inland highway being constructed with reduced long-term running cost.

It would be relatively simple to plan the economics of individual natural event repairs if there was some degree of regularity in the frequency of those events. But there are often misunderstandings in this regard. For example, a recent occurrence of a 100-year flood might give false assurance that a similar event will not occur for, say, a further 80 years or so.

In fact, the timing of extreme events is often quite irregular because they occur randomly. Something similar can be seen when a few raindrops fall on to a pavement. The drops fall randomly but give the appearance of clusters here and there. This apparent clustering of random events gives rise to surprising effects such as having two 100-year floods in 10 years, which is actually not all that improbable.

If we translate the same statistics to 100-year earthquakes then the possibility of an apparent cluster of big earthquakes has obvious implications for the national economy.

In reality, between-earthquake times at any one location are much more complicated than simple random events because of factors such as the time to build up stress in the rocks, and aftershocks from the main earthquakes. However, among all the complexity there is a big national picture of note from the infrastructure viewpoint: the average time between large earthquakes decreases considerably as you move further north through Northland.

The record of so few large earthquakes in the far north makes it difficult to be accurate as to just how much wider the earthquake spacings might be. It could well be that between-earthquake times for magnitude 6 quakes is 300 years at Cape Reinga, compared with perhaps 50 years at Hamilton.

This suggests that Kaitaia has special status as being New Zealand's most cost-effective town with respect to long-term running costs against earthquake damage, which should perhaps be reflected in reduced building strength specifications and insurance costs.

There are some risk factors from other hazards such as tropical cyclones and (though less likely) volcanic events. However, for long-term economics, Kaitaia seems a logical choice for locating various transferable government functions, with the important addition requirement of ensuring water supply against drought conditions such as those now being experienced in the north.

At the other end of the scale, it is more difficult to guess what might be the most expensive town for long-term running costs, which will be a combination of greatest overall risk and greatest amount of existing infrastructure to be maintained. Wellington is certainly a possible contender in this regard, taking into account the available information on its past earthquake frequency.